The central force problem in
non-relativistic classical mechanics is one of the most useful topics
in physics. Closely linked with the central force problem is the
Keplerian orbit theory which is a cornerstone for understanding
planetary motions in the solar system or motion of electrons near the
nucleus. In classical mechanics there is an important theorem called
the Bertrand's theorem which proposes that there can only be two types
of central potentials, the Coulomb type and the simple harmonic type,
which can produce stable, circular orbits for particles moving around
the potential source. A good presentation of the Bertrand's theorem can be
found in Ref. [1]}. The present article tries to
generalize the results of Bertrand's theorem when the orbiting
particle can have relativistic velocities.
